The Copernican Revolution Completed

Sir Isaac Newton

Galileo discovered some of the laws which describe the behavior of falling bodies, stating that freely falling bodies near the surface of the earth accelerate uniformly. Although he did not know the exact value, we now know that in a vacuum, for every second that a body falls, its speed increases by 980 cm/s. Newton unified these insights by showing that the force of gravitation that accelerates falling bodies near the earth is the same force that keeps the moon in its orbit around the earth and the planets in their orbits around the sun. His principles of mechanics and the law of gravitation are so general and powerful that in the century following his death they strongly influenced the prevailing philosophy. Many thinkers held that the basic rules of nature were finally known, and that all which remained was to fill in minor details. A philosophy of determinism developed in response to Newton's Third Law, holding that every action in the universe follows mechanistic laws from conditions immediately preceding the action.

Newton's view does not explain the motions of electrons around the nucleus of an atom. For this we need quantum theory. Newton's laws fail when compared to very fast speeds, as those nearing the speed of light, and to explain these phenomena we need relativity. However, Newton's Laws still are valid within their frame of reference. We could not have gone to the moon without knowing his laws. Now, we will try to explain these laws which are so fundamental to our understanding of astronomy. If you want a detailed look with links to Newton's Laws and discoveries, click on his image to the left, or you can also take a look at a nice biographical sketch by clicking on Newton.

Isaac Newton was born January 4, 1643 in Lincolnshire, London. He apparently had his birth date changed to December 25, 1642 to coincide with the death of Galileo. Newton believed that God appointed one individual each century to reveal God’s truth in science, and he was convinced that he was that person to succeed Galileo. He entered Trinity College at Cambridge in 1661 and so distinguished himself that he was appointed Lucasian Chair in 1669. The University was closed during the Plague of 1665-1666, during which time Newton did the math for gravity. Since the mathematical principles of his day were insufficient to resolve the gravity dilemma, Newton invented calculus that summer to make his formulas work. However, because he was more devoted to mathematics and optics, he put the gravity and mechanics word aside until much later. Robert Hooke (famous for his discovery of the cell) wrote a letter to Newton in 1679 asking for Newton's ideas about planetary motions. In 1684, Edmund Halley met with Newton and mentioned that he was struggling to explain how a planet moves with regard to a force which attracts it to the sun. Newton interest in planetary motion was rekindled, and he explained that he had worked this out years before, but because he lost his notes, he had to redo the math. He submitted his paper - The Mathematical Principles of Natural Philosophy, usually abbreviated PRINCIPIA in 1687. Most scientists and historians ascribe this book to be the greatest single intellectual effort of all time. In it he describes three laws:

1) MOMENTUM: Every body continues in a state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. Basically, a body tends to keep moving, and a stationary object tends to stay at rest. Momentum is a measure of the state of motion. Momentum depends on speed, and also on the amount of matter in a moving object, i.e., a car going 30 mph is harder to stop than a bike going 30 mph.. Newton then defined momentum as proportional to velocity, and defined this constant of proportionality as MASS. Mass is a quantity that characterized the amount of material in the body. The product of a body's mass and velocity is constant if no outside force is applied to it.

2) FORCE: The change of motion is proportional to the force impressed; and is made in the direction of the straight line in which that force is impressed. If a force acts on a body, it produces change in the momentum of the body that is in the direction of the applied force. The magnitude or strength of a force is defined as the rate at which it produces change in the momentum of the body on which it acts. Where there is no force, the change in momentum is zero. There are three ways in which momentum can change. Its velocity can change, or its mass, or both. Since the mass of a body typically does not change when the force is applied to it, a change of momentum usually results from a change in velocity. Thus, in the majority of cases: FORCE = MASS x ACCELERATION. If the acceleration occurs in the same direction as the velocity, the body speeds up. If the acceleration occurs in the opposite direction to the velocity, the body slows down. If the acceleration occurs at right angles to the velocity, only the direction of the motion of the body changes, and not the speed. Gravity accelerates a body in a direction toward the center of the more massive object, so the body falls faster and faster.

3) REACTION: To every action there is always an equal and opposite reaction: or, the mutual actions of two bodies upon each other are always equal, and act in opposite directions. All forces occur as pairs of forces that are mutually equal to and opposite each other. Any force which is exerted on an object will have a corresponding force which is exerted against it. When you push against an immobile car, it pushes back. When your feet are firmly planted, the reaction force of the car is transmitted through the you to the earth. Because the earth is so massive, the earth accelerates far less than the car. When a boy jumps off a table, the force pulling him down is a gravitational force between the boy and the earth. The boys jumps down 5 feet, but because the earth is so massive, it responds only a fraction of an amount. The same principal of reaction is seen in a batted ball and also in a rifle recoil. Here is also the principle of rockets - the force that discharges the exhaust gases from the rear of the rocket is accompanied by a force that shoves the rocket forward. The exhaust gases need not push against the air or earth; a rocket works best in a vacuum. In each case, a mutual force acts upon the two objects concerned; each object always experiences the same total change of momentum, but in opposite directions. Because momentum is the property of velocity and mass, the object of lesser mass will end up with proportionately greater velocity.

Ordinary momentum is the product of mass & velocity

Angular momentum is the product of mass, velocity, and the distance of the fixed point around which an object turns. If you do not change any value, the system perpetuates. If you reduce the distance, the mass stays the same, but the velocity increases - like a skater doing a final sitz spin.

Newton's Principia is of such length that it becomes difficult to even give a summary of it here. A personal friend of mine mistakenly joined a "book of the month club" and began receiving volumes of the Principia. After an entire year, he was the owner of 21 volumes of Newton's work. My friend is a swimming coach and has no interest in Newtonian Physics, so the set sits idly on his bookshelf in the loft of his home.

THE LAW OF UNIVERSAL GRAVITATION was perhaps his most important contribution to Astronomy. Kepler nearly discovered this force. Galileo demonstrated the property of gravity in his experiments and papers on falling bodies. Neither were able to solve the mathematical explanation for such observed actions. Legend hold that an apple fell on Newton's head while he was resting near a cemetery. Newton pondered the fallen apple, and then looked at the adjacent graves and recognized the "gravity" of this apple's demise, and hence the name came to his head. In reality, apples may have fallen on Newton's head, but they did not incite great interest. Newton applied his motion laws to the orbit of the moon. He reasoned that the moon should be moving in a straight line and continue to do so unless acted upon by another force. Somehow, another force must be causing the moon to follow a curved path, and do so indefinitely. The moon is not orbiting around the moon as much as it is falling toward the earth an exact distance equal to the distance it is moving forward in a straight line. There must be a force between earth and moon which is causing the forward and downward motions to result in a curved path, and he described this force as the mutual attraction, or "Gravity" between earth and moon.
Between any two objects anywhere in space there exists a force of attraction that is in proportion to the product of the masses of the object and in inverse proportion to the square of the distance between them.

F = G m1m2/d^2

F is the force of gravity between two objects of mass, m1 and m2
G is Newton’s constant number which is in every equation to make the math work (G = 6.67 x 10^-11 N m^2/kg^2)
m refers to the masses of the two bodies between which gravity acts
d is the distance between those two bodies of mass

Newton derived many other mathematical formulae, but two more are given below. The first describes the manner in which anyone can determine the velocity of escape from any object of mass in space.

Ve = 2GM/R)^-2

The other gives the orbital velocity for any planet whose circumference of orbit is known.

V = 2(Pi)r/P

where P is the orbital period measured in years, as in Kepler's Three Laws.

From these Laws, you can discover the force of Gravity between you and the Earth, assuming you know your mass in kg, since the mass of the Earth is 59.74x10e23 kg, and the distance between you and the center of the Earth is 6388 km. Of critical importance here is to remember the units which are used in these formulae. The units of mass are measured in kilograms (kg), but the units of distance are measured in meters (m), so the radius would need to be multiplied by 1000 to allow the equation to work.

More relevantly, you can derive the center of mass of a binary system ... The Sun and the Earth, the Earth and the Moon, an eclipsing binary star system. You can derive a center of mass between any two objects by applying the formula: m1d1 = m2d2 where d1 + d2 = radius between object 1 and object 2. This is useful in determining the center of mass in the Earth-Moon system. The mass of the Earth is 5.974 x 10^24 kg and the mass of the Moon is 7.348 x 10^19 kg. The Earth radius is 6378 km and the Moon's radius is 1738 km, with the average distance between the two objects being 384,400 km.

When talking about celestial bodies, the center of mass has a special relevance: when a moon orbits around planet, or a planet orbits around a star, both of them are actually orbiting around their center of mass, called the barycenter, see two-body problem<-- a Wikipedia problem that you can look to for more details

where : r(1) = r(total) m(2)/m(1)+m(2)

r(1) is the distance from body 1 to the barycenter
r(total) is the distance between the two bodies
m(1) and m(2) are the masses of the two bodies.
Some examples:

Earth-Moon system: the Moon's mass is 0.0123 that of Earth. Put Earth in position 0, mass 1 (here we use an arbitrary mass unit. It does not matter, provided that we use the same unit for the Moon). The Moon is at an average distance of 384400 km from the Earth. Then the center of mass is at:

0 x 1 + 384,400 km x 0.0123/1 + 0.0123 = 4761 km

from the Earth's center. Thus, as opposed to the Earth standing "still" and the Moon moving, both of them move around a point about 1700 km below the Earth's surface.

The results of this little exercise demonstrate that the center of gravity for the Earth-Moon system is actually inside the Earth, but also that the Earth is slowly wobbling as the Moon orbits. This gives the Earth a small back-and-forth motion that is measurable. In the case of the Sun, the Earth's masses is incredibly small by comparison, as seen below:

Sun-Earth system: put Sun in position 0, mass=333,000 times the Earth. Earth in position 150,000,000 km, mass=1. Center of mass is 450 km from the Sun center. Here, the large mass difference between the two bodies makes the center of mass lie almost at the center of the Sun. The Earth does make the Sun wobble, but it is barely perceptible! But, when we look at the effect of Jupiter on the Sun:
Sun-Jupiter system: put Sun in position 0, mass = 333,000 Earths. Jupiter in position 778,000,000 km, mass=318 Earths. Center of mass is 742,000 km from the Sun center, 46,000 km outside its surface. As Jupiter does its 11 year orbit, the Sun does a 1.5 million km orbit around the center of mass.

This last result shows that the Sun wobbles a great distance due to the gravitational attraction of Jupiter and the location of the barycenter of the Jupiter/Sun system. It is this kind of wobble that Geoff Marcy looks for in distant stars. If he can find a star that wobbles back and forth and determine the period of that wobble, then he can discern that a planet is orbiting that distant star, figure out the length of the orbit, and even determine the relative mass and distance of the planet. In this manner, astronomers find extra-solar planets!

To calculate the actual motion of the Sun, you would need to sum all the influences from all the planets, comets, asteroids, etc. of the solar system. To an alien astronomer watching the complicated movement of the Sun, it might be impossible to determine the number of planets, their masses, and relative locations from a star far away!

Applying the Laws of Newtonian Physics to High School Dating Relationships

If knowing the force of gravity between you and the earth, as well as the speed you would need to jump at in order to escape the earth's gravity is not relevant to you, then consider your dating relationship ... if you have any. Your attraction to that significant other is merely a physical force called mutual attraction or gravity. The closer you get, the stronger the force, and significantly so due to the effect of the squaring of the distance between you two. The continuing approach of two of you toward each other, resulting in the loving embrace and tender and compassionate kiss is merely reduced to a physical force of gravity which can be mathematically explained. Your date might be lost in emotional thoughts, but your mind is pondering the strength of the gravitational force. You want desperately to learn about the possibility of a long-term relationship but in order to solve the math, you need to know the mass of your partner. You stop the kiss and embrace and ask the all-important question, "What is your mass in kg?" This results in a slap to your face and a most certain termination to your relationship. If your date is just as excited about knowing the force of gravity with you, then you know you are well on your way! Love is nothing more than gravitational attraction between two bodies of mass. Instead of flowers, you may exchange handheld calculators on your anniversaries, go out an eat everything on the McDonald's menus, and live happily ever after.

As you read in the text of these laws and others, keep in mind that gravity is so very important in understanding how celestial objects move, and how stars work. Newton was a brilliant man, some even contending that he was the most intelligent man of all time, but alas with all of his brain power, he had a few shortcomings. Sir Isaac believed that he was the singular appointed spokesman from God to the world, and that only he had correct interpretations. He did not endear himself to many fellow scientists due to his own arrogance. He also practiced alchemy in a vain attempt to convert lead into gold.

Applying Newton's Laws to the Velocity of a Satellite and to the Velocity of Escape of a rocket

In the in-house course, we spend some time using Newton's formula to determine some rocket science questions (everyone wants to be a rocket scientist these days, especially after watching October Sky and seeing how Homer Hickum used his brain instead of his braun to get from Coalwood, WV, win the Science Fair, get a college scholarship, and work for NASA). To see how these laws are applied, and try your hand at what rocket scientists do, please move to Gravity Problems.

Review of science/religion clash:

The early history of astronomy also offers a peek into a terrific struggle for power between the Roman Empire and the Holy Roman Empire. While the emperor controlled the people with military strength and taxes, the Pope controlled the people with religious regulations and fear of eternal hopelessness. The Reformation and the Astronomical Revolution were in the same century and common people began to rethink ideas which had gone unchallenged during the previous millennium. It was just as important to accurately interpret the Scriptures as Martin Luther was asking as it was to accurately interpret celestial motions as Copernicus was asking. Both men believed in a literal God. Both were soundly criticized by the Roman Catholic Church. Both men dared to ask questions and offer alternative viewpoints than those widely held but poorly defended. In my in-house Astronomy class, we would watch the movie "October Sky," not only because it is a true story, but to demonstrate the power of new thinking. Homer Hickum dared to think he might use his mind to get a scholarship and get out of Coalwood. For years, football was the only ticket to college, and most worked the mines. Homer built rockets, went against his own father. He was inspired by a teacher to dream big, solve problems, and stick with his hopes. The same principles which resulted in the entire world being turned around by the writings of Martin Luther and Nicolaus Copernicus should give anyone today the same encouragement. Dare to think different. Dare to dream big. Then dare to do something about it.

Below is a short list of questions which can also be accessed at theCopernican Revolution Quiz.

  1. How was the solar system model of Copernicus different from that of Ptolemy? How was it similar?

  2. When did Copernicus publish his theories, and why did he wait so long to do so?

  3. What was the value of Martin Luther's departure from Roman Catholicism to Copernicus?

  4. What was Tycho Brahe’s greatest contribution to Astronomy?

  5. What happened to Tycho's nose?

  6. How did Kepler correct the heliocentric model of Copernicus?

  7. Which particular discovery of Galileo most angered Church leaders?

  8. Of the 3 variables in Newton’s Law of Gravity, which will have the greatest effect if changed?

  9. What is the force of gravity between you and the cloudtops of Jupiter.

  10. What lesson can be learned from the writings of Martin Luther and Nicolaus Copernicus?

You have completed the History of Astronomy Unit. By no means do I believe this unit to be complete, but it will serve to give you a feel for the tremendous upheaval caused by the Copernican heliocentric model.

Martin Luther encouraged people to think differently. Instead of blindly accepting what a priest told them the truth to be, read for yourselves and make your own conclusions.

Copernicus dared to rethink the Ptolemaic geocentric model, proposing a heliocentric view. Like Luther, he dared to think differently.

Tycho took detailed notes of the motion of planets against the starry background. While the maps were excellent, he misinterpreted his notes and drew incorrect conclusions. His failure to listen to the opinions of others is an example of personal ego clouding good judgment.

Kepler reevaluated the work of Tycho and offered the correct interpretation of the data. Copernicus was almost completely right. Kepler gave some mathematical proof for the Copernican model.

Galileo provided the observational proof of the Copernican model and Kepler's Laws, but at great emotional and spiritual cost.

Finally, Isaac Newton provided mathematical proofs and explanatory Laws which confirmed the heliocentric model and Galileo's observations. The Astronomy Revolution was completed ... and all accomplished between 1543 and 1687! I once again cannot emphasize enough the power of original thought. You are now to write the Grad Standard Paper for this course. This paper should demonstrate your understanding of the Copernican Revolution and its relationship with the Protestant Reformation.

A general overview of the universe as we now know it to be.
Sun is center of solar system
Nine planets revolve around the sun
Ninety-one known moons are orbiting the planets
Planets and moons are mere reflectors, while the sun is a light and heat creator
The Sun lies in an arm of Milky Way
The Milky Way contains approximately 200 billion stars
Stars differ in composition, size, temperature, energy output, and age
Vast distances separate stars and even greater distances are between neighboring galaxies
We measure distances to planets in our solar system in Astronomical Units
1 AU = distance from earth to sun = 149,600,000 km
We measure distances to stars and galaxies in Light Years
1 LY = distance light travels in 1 year = 300,000 km/sec x 60 sec/min x 60 min/hr x 24 hr/day x 365.25 day/yr = this is over 9,400,000,000,000 km

Back to Copernicus, Martin Luther, Introduction to the History Unit, or Syllabus, or Home page. Just make sure you take the Copernican Revolution Quiz.

Since this represents the conclusion to the History Unit as far as Astronomers is concerned, it is time to move ahead into a lesson about Light and Telescopes. The goal of the next lesson is to understand the properties of starlight and the instruments that are used to study celestial objects.

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